Results on Initial Value Problems for Random Fuzzy Fractional Functional Differential Equations

Abstract

In this paper random fuzzy fractional functional differential
equations (RFFFDEs) with Caputo generalized  Hukuhara
differentiability are introduced. We present existence and
uniqueness results for RFFFDEs using the idea of successive
approximations. The behaviour of solutions when the data of the
equation are subjected to errors is discussed. Furthermore, the
solution to random fuzzy fractional functional initial value problem
under  Caputo-type fuzzy fractional derivatives by a modified
fractional Euler method (MFEM) is presented. The results are
illustrated with examples.